We further define filtering in graph signal processing [1]} as \(x_f = g(L) x\) , where the filter \(g(L)\)  is an operator defined through the graph Laplacian matrix, and \(x_f\)  represents a filtered graph signal.The choice of the filter \(g(\cdot )\)  drives different spectral characteristics of the graph signals. For example, a heat kernel \(g(L) = e^{-\tau L}\)  models a graph based on the nature of the spread of heat through the graph, usually emphasizing global graph properties. On the other hand, a high pass filter like \(g(L)= L^2\)  takes more local phenomena into account, prioritising high graph frequencies. A graph filter can be represented in matrix form as
\(g(L) &= U \hat{G} U^T \) 
